Heat sinks and heat slugs have been used to remove heat from the back of high power integrated circuit chips, as shown in U.S. Pat. Nos. 5,394,298 and 5,297,006. The thermal performance of these systems has not been adequate to accommodate very high power chips, however. The problem has been compounded for semiconductor structures in which chips are stacked. Thus, a better solution is needed that provides for improved heat removal, and this solution is provided by the following invention.